Mathematical models of carcinogenesis that are designed to capture important features of the multistage process, from normal cells, via expanding intermediate cell populations, to the appearance of malignant tumors, offer the opportunity to study in greater detail the effects of specific interventions that affect critical biological processes involved in carcinogenesis. The main focus of this proposal is therefore the development of tools and methods for the quantitative evaluation of possible prevention and intervention strategies and to apply them to colorectal cancer. These tools and methods will be based on stochastic models of carcinogenesis that reflect insights gained into the pathogenesis of colon cancer over the past decade, as well as extensions of these models that allow for the incorporation of additional (putative) pathways associated with genomic instability. To achieve this goal with confidence, it is important that the models used for this purpose give satisfactory descriptions of the incidence of colon cancer in the general population. A challenge, so far unmet, is that these models also be consistent with observations on the prevalence and size distribution of adenomatous polyps, pathologically well-characterized precursor lesions to colorectal tumors. These polyps are also the subject of specific cancer screening and intervention strategies. This motivates the mathematical development of statistical and computational tools to analyze relevant data sets: (1) the SEER registry data on colorectal cancer (CRC) incidence, (2) CRC incidence in a large prospective cohort of women (the Shanghai study), (3) the Minnesota Cancer Prevention Research Unit (CPRU) polyp data, and (4) data from a case-control study of CRC and the role of sigmoidoscopy conducted at the Fred Hutchinson Cancer Research Center. Models derived from these analyses and the computational tools developed will facilitate the prediction of benefits associated with specific screening, prevention and intervention strategies. [unreadable] [unreadable]